Defects in Chern-Simons theory, gauged WZW models on the brane, and level-rank duality

We consider Hanany-Witten setups of 3- and 5-branes in type IIB string theory that realize N=(1,0),(2,0) and (1,1) gauged WZW models in 1+1 dimensions. The gauged WZW models arise as theories residing on the boundary of D3 branes ending on D5 branes. From the point of view of low energy dynamics the D5 branes play the role of half-BPS co-dimension-1 defects (domain walls) in 3d N=1 or N=2 Chern-Simons theories. Extending the analysis of previous works on the subject of boundary conditions in (supersymmetric) Chern-Simons theory, we discuss in detail the field theory construction of a large class of Chern-Simons domain wall theories and its embedding in open string dynamics. Finally, we exhibit how standard brane moves that result to 3d Seiberg duality, translate in our setup to a generalized level-rank duality in gauged-WZW models.